Cases of Campana's orbifold conjecture and Vojta's general abc conjecture for orbifold entire curves


We study Campana’s orbifold conjecture for finite ramified covers of $\mathbb P^2$ with three components admitting sufficiently large multiplicities. We also prove a truncated second main theorem of level one for analytic maps into $\mathbb P^2$ intersecting the coordinate lines in sufficiently high multiplicities. In particular, the exceptional set for the later result can be described explicitly.

This is joint work with Ji Guo.